{"id":"https://openalex.org/W2171876361","doi":"https://doi.org/10.1017/s0960129500000578","title":"Languages under concatenation and shuffling","display_name":"Languages under concatenation and shuffling","publication_year":1994,"publication_date":"1994-12-01","ids":{"openalex":"https://openalex.org/W2171876361","doi":"https://doi.org/10.1017/s0960129500000578","mag":"2171876361"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129500000578","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129500000578","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025342506","display_name":"Steven T. Tschantz","orcid":"https://orcid.org/0000-0002-6803-7673"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Steven T. Tschantz","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University, Nashville, TN 37240"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, Nashville, TN 37240","institution_ids":["https://openalex.org/I200719446"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025342506"],"corresponding_institution_ids":["https://openalex.org/I200719446"],"apc_list":null,"apc_paid":null,"fwci":1.4615,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.83304442,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":"4","first_page":"505","last_page":"511"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.738200306892395},{"id":"https://openalex.org/keywords/concatenation","display_name":"Concatenation (mathematics)","score":0.7071442604064941},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.6276532411575317},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5912042856216431},{"id":"https://openalex.org/keywords/shuffling","display_name":"Shuffling","score":0.5763964653015137},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5188676118850708},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.475948303937912},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36362284421920776},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1970480978488922},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07451227307319641}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.738200306892395},{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.7071442604064941},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6276532411575317},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5912042856216431},{"id":"https://openalex.org/C167927819","wikidata":"https://www.wikidata.org/wiki/Q1930567","display_name":"Shuffling","level":2,"score":0.5763964653015137},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5188676118850708},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.475948303937912},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36362284421920776},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1970480978488922},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07451227307319641},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0960129500000578","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129500000578","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1981404622","https://openalex.org/W1985495277"],"related_works":["https://openalex.org/W4213239787","https://openalex.org/W4377131110","https://openalex.org/W2114337652","https://openalex.org/W4388857216","https://openalex.org/W2046590706","https://openalex.org/W1587991081","https://openalex.org/W2949444602","https://openalex.org/W2120641958","https://openalex.org/W2946585142","https://openalex.org/W3120719177"],"abstract_inverted_index":{"The":[0,120],"shuffle":[1,121],"product":[2,122],"of":[3,14,17,88,105,123,137],"two":[4],"words":[5,16,41,91],"u":[6,58,82,98,106,139,143],"and":[7,36,68,99,107,126,146],"v,":[8],"denoted":[9,129],"u\u2016v,":[10],"is":[11,85,134],"the":[12,18,86,103,135],"set":[13,87],"all":[15,89,138],"form":[19],"x":[20,24,29,42,46,60,62,65],"1":[21,23,43,50,61,72],"y":[22,26,31,49,53,71,73,76],"2":[25,27,63,74],"\u2026":[28,45,52,64,75],"n":[30,32,35,47,54,66,77],"for":[33,37,142],"some":[34,38],"(possible":[39],"empty)":[40],",":[44,48,51,55,67,128,133],"such":[56],"that":[57,92,102],"=":[59,70],"v":[69,84,100,108,141,147],".":[78,150],"In":[79],"other":[80],"words,":[81],"\u2016":[83,131,140],"possible":[90],"can":[93],"be":[94],"obtained":[95],"by":[96],"merging":[97],"so":[101],"letters":[104],"separately":[109],"maintain":[110],"their":[111],"original":[112],"orders":[113],"but":[114],"are":[115],"allowed":[116],"to":[117],"alternate":[118],"arbitrarily.":[119],"languages":[124],"L":[125,130,145],"M":[127,132,149],"union":[136],"\u2208":[144,148]},"counts_by_year":[{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}